Sin3x-sinx=0 решаем ребята)

[latex]\sin 3x-\sin x=0\\3\sin x-4\sin^3x-sinx=0\\2\sin x-4\sin^3x=0\\2\sin x(1-2\sin^2x)=0\\\sin x=0\\x=\pi n,n\in\mathbb{Z}\\\sin x=\pm\cfrac{1}{\sqrt{2}}\\\sin x=\cfrac{1}{\sqrt{2}}\\x=\cfrac{\pi}{4}+2\pi n,n\in\mathbb{Z}\\x=\cfrac{3\pi}{4}+2\pi n,n\in\mathbb{Z}\\\sin x=-\cfrac{1}{\sqrt{2}}\\x=\cfrac{5\pi}{4}+2\pi n,n\in\mathbb{Z}\\x=\cfrac{7\pi}{4}+2\pi n,n\in\mathbb{Z}[/latex]